Furthermore, we propose a model to reproduce another type of self-oscillation found in the present study.We perform experiments on an active chiral fluid system of self-spinning rotors in a confining boundary. Along the boundary, actively rotating rotors collectively drive a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. https://www.selleckchem.com/products/carfilzomib-pr-171.html Flow strength initially increases then decreases with rotor density (quantified by area fraction ?); peak strength appears around a density ?=0.65. Boundary curvature plays an important role flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary. Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions.We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of the dynamics and the lack of describability of the structure in the Poincaré plane constructed from a given time series. As for the former, we use the permutation entropy S_p, while for the latter, we introduce an indicator, the structurality Δ, which accounts for the fraction of visited points in the Poincaré plane. The complexity measure thus defined as the sum of those two components is validated by classifying in the (S_p,Δ) space the complexity of several benchmark dissipative and conservative dynamical systems. As an application, we show how the metric can be used as a powerful biomarker for different cardiac pathologies and to distinguish the dynamical complexity of two electrochemical dissolutions.In this paper we propose a method, which is based on equivariant moving frames, for development of high-order accurate invariant compact finite-difference schemes that preserve Lie symmetries of underlying partial differential equations. In this method, variable transformations that are obtained from the extended symmetry groups of partial differential equations (PDEs) are used to transform independent and dependent variables and derivative terms of compact finite-difference schemes (constructed for these PDEs) such that the resulting schemes are invariant under the chosen symmetry groups. The unknown symmetry parameters that arise from the application of these transformations are determined through selection of convenient moving frames. In some cases, owing to selection of convenient moving frames, numerical representation of invariant (or symmetry-preserving) compact numerical schemes is found to be notably simpler than that of standard, noninvariant compact numerical schemes. Further, the accuracy of these invariant compact schemes can be arbitrarily set to a desired order by considering suitable compact finite-difference algorithms. Application of the proposed method is demonstrated through construction of invariant compact finite-difference schemes for some common linear and nonlinear PDEs (including the linear advection-diffusion equation in one or two dimensions, the inviscid Burgers' equation in one dimension, viscous Burgers' equation in one or two dimensions, spherical Burgers' equation in one dimension, and shallow water equations in two dimensions). Results obtained from our numerical simulations indicate that invariant compact finite-difference schemes not only inherit selected symmetry properties of underlying PDEs, but are also comparably more accurate than the standard, noninvariant base numerical schemes considered here.We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the two-dimensional Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.In this paper, we have proposed a statistical procedure for detecting transitions of the mean-square-displacement exponent value within a single trajectory. With this procedure, we have identified three regimes of proteins dynamics on a cell membrane, namely, subdiffusion, free diffusion, and immobility. The fourth considered dynamics type, namely, superdiffusion was not detected. We show that the analyzed protein trajectories are not stationary and not ergodic. Moreover, classification of the dynamics type performed without prior detection of transitions may lead to the overestimation of the proportion of subdiffusive trajectories.We study the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated on a problem of population establishment, which is important in ecology. At the deterministic level, the model we study gives rise to a critical population size beyond which the system experiences establishment. Notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations. Here we consider two prototypical examples of a time-varying environment a temporary change in the environment, and a periodically varying environment. By employing a semiclassical approximation we compute, within exponential accuracy, the change in the establishment probability and mean establishment time of the population, due to the environmental variability. Our analytical results are verified by using a modified Gillespie algorithm which accounts for explicitly time-dependent reaction rates. Importantly, our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations.